IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the percent of individuals with the IQ's in the following ranges: (Use the Empirical Rule 68-95-99.7)

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**Understanding IQ Score Distribution Using the Empirical Rule**

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the percent of individuals with IQs in the following ranges:

*Use the Empirical Rule (68-95-99.7)*

1. **Between 70 and 100:**
   
   [        ] %

2. **Within one standard deviation of the mean:**
   
   [        ] %

3. **Above 145:**
   
   [        ] %

4. **Below 100:**
   
   [        ] %

**Explanation of the Empirical Rule:**

The Empirical Rule, also known as the 68-95-99.7 rule, is used to explain the distribution of data in a normal distribution. Here’s a breakdown:

1. **68% of the data** falls within one standard deviation (σ) of the mean (μ). Mathematically, this is between (μ - σ) and (μ + σ).
2. **95% of the data** falls within two standard deviations of the mean. This range is between (μ - 2σ) and (μ + 2σ).
3. **99.7% of the data** falls within three standard deviations of the mean. The range here is (μ - 3σ) to (μ + 3σ).

Given the mean (μ) is 100 and the standard deviation (σ) is 15 for IQ scores, use these concepts to fill in the blanks.
Transcribed Image Text:**Understanding IQ Score Distribution Using the Empirical Rule** IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the percent of individuals with IQs in the following ranges: *Use the Empirical Rule (68-95-99.7)* 1. **Between 70 and 100:** [ ] % 2. **Within one standard deviation of the mean:** [ ] % 3. **Above 145:** [ ] % 4. **Below 100:** [ ] % **Explanation of the Empirical Rule:** The Empirical Rule, also known as the 68-95-99.7 rule, is used to explain the distribution of data in a normal distribution. Here’s a breakdown: 1. **68% of the data** falls within one standard deviation (σ) of the mean (μ). Mathematically, this is between (μ - σ) and (μ + σ). 2. **95% of the data** falls within two standard deviations of the mean. This range is between (μ - 2σ) and (μ + 2σ). 3. **99.7% of the data** falls within three standard deviations of the mean. The range here is (μ - 3σ) to (μ + 3σ). Given the mean (μ) is 100 and the standard deviation (σ) is 15 for IQ scores, use these concepts to fill in the blanks.
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